A note on “Regularity lemma for distal structures”
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- Proc. Amer. Math. Soc. 144 (2016), 3573-3578 Request permission
Abstract:
In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely model-theoretic proof of this fact, though with no explicit bounds.References
- Noga Alon, János Pach, Rom Pinchasi, Radoš Radoičić, and Micha Sharir, Crossing patterns of semi-algebraic sets, J. Combin. Theory Ser. A 111 (2005), no. 2, 310–326. MR 2156215, DOI 10.1016/j.jcta.2004.12.008
- Artem Chernikov and Sergei Starchenko, Regularity lemma for distal structures, Journal of the European Mathematical Society, (to appear).
- Ehud Hrushovski, Anand Pillay, and Pierre Simon, Generically stable and smooth measures in NIP theories, Trans. Amer. Math. Soc. 365 (2013), no. 5, 2341–2366. MR 3020101, DOI 10.1090/S0002-9947-2012-05626-1
- Pierre Simon, Distal and non-distal NIP theories, Ann. Pure Appl. Logic 164 (2013), no. 3, 294–318. MR 3001548, DOI 10.1016/j.apal.2012.10.015
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Additional Information
- Pierre Simon
- Affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
- MR Author ID: 942320
- Email: simon@math.univ-lyon1.fr
- Received by editor(s): September 16, 2015
- Published electronically: March 18, 2016
- Additional Notes: This research was partially supported by ValCoMo (ANR-13-BS01-0006).
- Communicated by: Mirna Dz̆amonja
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3573-3578
- MSC (2010): Primary 03C45, 03C98; Secondary 05C35, 05C69, 05D10
- DOI: https://doi.org/10.1090/proc/13080
- MathSciNet review: 3503725